Short answers, pulled from the story.
Deductive reasoning is the process of drawing inferences where the truth of the premises guarantees the truth of the conclusion; it is impossible for the premises to be true and the conclusion false. Inductive reasoning, by contrast, offers only probabilistic support, meaning the conclusion can still be false even when the premises are true and the argument is well-formed.
Modus ponens, the primary rule of deductive inference, draws the consequent of a conditional statement when the antecedent is confirmed. Modus tollens runs the opposite direction, concluding that the antecedent is false when the consequent is shown to be false. In a meta-analysis of 65 studies, 97% of subjects evaluated modus ponens correctly, compared to only 72% for modus tollens.
A deductive argument is valid if it is impossible for its premises to be true while its conclusion is false, regardless of whether the premises are actually true. An argument is sound only when it is both valid and all its premises are in fact true.
Gerhard Gentzen and Stanislaw Jaskowski developed the first systems of natural deduction in the 1930s. Their goal was to present deductive reasoning in a way that closely mirrors how actual reasoning takes place, replacing axiom schemes with specific rules of inference for each logical constant.
In Peter Wason's experiment, participants were shown four cards displaying D, K, 5, and 7, and asked which cards to flip to test a conditional rule. Only about 10% chose correctly. When the same logical structure was reframed around a beer-drinking age rule, 74% answered correctly, showing that reasoning performance is heavily influenced by the concrete content of a problem, not just its abstract logical form.
Deductivism is the philosophical position that only deductive inferences are rationally acceptable forms of reasoning, denying that inductive reasoning provides genuine support for conclusions. Karl Popper's falsificationism is a closely related view, holding that a scientific theory remains viable until one of its deductive consequences is falsified by empirical observation, making deduction sufficient for discriminating between competing hypotheses.